Elsevier Editorial System(tm) for International Journal of Research in Marketing Manuscript Draft Manuscript Number: IJRM-D-11-00481R3 Title: A Comparison of Different Pay-Per-Bid Auction Formats Article Type: Full Length Article Corresponding Author: Dr. Ju-Young Kim, Corresponding Author's Institution: Goethe-University Frankfurt First Author: Ju-Young Kim Order of Authors: Ju-Young Kim; Tobias Brünner; Bernd Skiera; Martin Natter Abstract: Pay-per-bid auctions are a popular new type of Internet auction that is unique because a fee is charged for each bid that is placed. This paper uses a theoretical model and three large empirical data sets with 44,614 ascending and 1,460 descending pay-per-bid auctions to compare the economic effects of different pay-per-bid auction formats, such as different price increments and ascending versus descending auctions. The theoretical model suggests revenue equivalence between different price increments and descending and ascending auctions. The empirical results, however, refute the theoretical predictions: ascending auctions with smaller price increments yield, on average, higher revenues per auction than ascending auctions with higher price increments, but their revenues vary much more strongly. On average, ascending auctions yield higher revenues per auction than descending auctions, but results differ strongly across product categories. Additionally, revenues per ascending auction also vary much more strongly. Forthcoming IJRM Volume 31 #4 (2014)
Transcript
Elsevier Editorial System(tm) for
International Journal of Research in Marketing
Manuscript Draft
Manuscript Number: IJRM-D-11-00481R3
Title: A Comparison of Different Pay-Per-Bid Auction Formats
Pay-per-bid auctions offered by retailers, such as Quibids, Bidcactus and MadBid, are
exciting, fast-paced business-to-consumer online auctions that are attracting significant interest
from consumers, popular press and start-up companies. Unlike other well-known auctions sites,
such as eBay, pay-per-bid auctions charge a fee for each bid that is placed, regardless of whether
one wins the auction. Additionally, a bid placed increases the price by a certain increment that is
chosen by the auctioneer.
At first glance, fee-based bidding does not sound attractive because the bidder encounters the
risk of having to pay bidding fees without winning the auction. However, the compelling part of
this model is that the bidders who win an auction can potentially save more than 99% off the
current retail price (CRP) of the product. For example, on MadBid.com, a new MINI One car was
sold for €8.47 rather than its retail price of €15,000. Similarly, a new Kymco scooter, which
regularly sells for €1,240, was sold for €0.40.
Popular magazines, newspapers and online blogs are replete with heated discussions
regarding this emerging type of auction.1 Although some commentators are enthusiastic about the
attractive deals offered by pay-per-bid auctions and how enjoyable they are, others strongly warn
consumers against participating in them. Such commentators point to potentially huge losses for
1 For magazines, see for example, Last, Jonathan V. (February 23, 2009) “Take a chance on an auction; Swoopo and
the rise of Entertainment Shopping” in The Weekly Standard; (December, 2011) “Can you buy products dirt cheap on QuiBids? Behind the hype” in Consumer Reports. For newspapers, see for example, King, Marc (January 28, 2012) “How penny auction websites can leave you with a hole in your pocket” in The Guardian; Zimmerman, Ann (August 17, 2011) “Penny auctions draw bidders with bargains, suspense” in The Wall Street Journal; Choi, Candice (June, 24, 2011) “Penny auction sites could cost a chunk of change” in The Washington Times; ConsumerReports.org (December 2011) “With penny auctions, you can spend a bundle but still leave empty-handed”; McCarthy, John (June, 2, 2011) “Penny auctions promise savings, overlook downsides” in USA Today; Migoya, David (January 25, 2010) “BARGAIN BIDDERS On penny auction sites, buyers can get gift cards for a fraction of face value -- or pick up a new addiction” in The Denver Post; and Thaler, Richard H. (November 15, 2009) “Paying a Price For the Thrill of the Hunt” in The New York Times. For blogs, see for example, http://www.foxbusiness.com/personal-finance/2012/07/10/online-auction-virtual-bargain-or-real-rip-off/, http://www.scambook.com/blog/2012/07/penny-auction-fraud-alert-how-you-can-lose-by-winning/, http://www.usatoday.com/tech/columnist/kimkomando/2011-05-13-komando-penny-auctions_n.htm, http://www.thesimpledollar.com/2010/11/20/a-deeper-look-at-quibids-and-why-i-dont-think-its-worth-it/, and http://www.theregister.co.uk/2009/01/02/swoopo_startrup/.
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bidders as a result of the high bidding costs, which can easily be in the range of several hundred
dollars per auction. However, all commentators have based their conclusions on a fairly limited
number of observations, some of which are quite anecdotal.
Furthermore, auctioneers lack knowledge regarding how different auction formats influence
their profitability. They frequently adjust their auction formats, and many auctioneers, such as the
pioneer of this type of auction, Swoopo, have become bankrupt. Thus far, only a few researchers
have analyzed pay-per-bid auctions by developing theoretical models (Augenblick, 2012; Gallice,
2011; Platt, Price, & Tappen, 2013) and by testing these models with actual sales data. Others
have empirically compared the effect of the buy-now price feature on bidders' behavior in
ascending penny auctions (Reiner, Natter, & Skiera, 2014). Analysis of the economic effects of
different pay-per-bid auction formats that differ in the sizes and signs of price increments has
thus far been neglected. We are the first researchers to close this gap.
We aim to theoretically and empirically assess the economic effects of different pay-per-bid
auction formats. In particular, we compare different price increments (penny vs. ten-cent
auctions) of ascending auctions as well as of ascending and descending pay-per-bid auctions.
Therefore, we adapt and extend previous theoretical models, formulate predictions regarding the
influence of auction formats on auctioneer revenues and empirically analyze them using three
unique and large empirical data sets. Our data include the results of 44,614 ascending pay-per-bid
auctions and 1,460 descending pay-per-bid auctions along with 1,142,738 bids.
The remainder of this manuscript is structured as follows. In the next section, we compare the
most prominent pay-per-bid auctioneers and outline previous literature on pay-per-bid auctions.
In Section 3, we describe our theoretical models and formulate predictions for the economic
effects of different pay-per-bid auction formats. We investigate the economic influence of
different formats of ascending pay-per-bid auctions in Section 4 and those for descending pay-
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per-bid auctions in Section 5. In Section 6, we compare the results of ascending and descending
auctions. Section 7 summarizes our findings, discusses implications and points to topics for
future research.
2. Pay-per-Bid Auctions
Pay-per-bid auctions are characterized by the association of bidding with tangible costs.
Using traffic data (May 5 to August 5, 2013) from Alexa.com, Table 1 outlines some of the
largest pay-per-bid auctioneers (with a reach of more than 0.001% of all global Internet users)
and the characteristics of their auctions. All ascending auctioneers begin with a price of zero, but
they differ by how much they change the price for each bid. Quibids offer various price
increments that range from €0.01 to €0.15, whereas others increase the price by only €0.01. The
start price of descending auctions is equal to the CRP. Bidding fees are substantial in all auction
formats, ranging from €0.50 to €1.50.
Table 1
Comparison of the Most Popular Pay-per-Bid Auctions
Knowledge of ascending pay-per-bid auctions in particular is currently growing. Augenblick
(2012), Hinnosaar (2010) and Platt et al. (2013) were the first researchers to provide theoretical
models of ascending pay-per-bid auctions. Independently of one another, they show that any
subgame perfect equilibrium of an ascending pay-per-bid auction that receives more than one bid
must be in mixed strategies. A mixed strategy in this context means that bidders randomly choose
between bidding and not-bidding in each round of the auction.
According to their theoretical models, Augenblick (2012) and Platt et al. (2013) find
deviations with actual revenues being well above expected revenues. Therefore, Platt et al. (2013)
extend their model to allow for risk preferences (risk-loving/risk-averse vs. risk-neutral), which
leads to expected revenues that better match actual revenues. Byers, Mitzenmacher, and Zervas
(2010) build on the theoretical model developed by Platt et al. (2013) and Augenblick (2012) and
analyze information asymmetries across bidders. Their model shows that when bidders
underestimate the true number of bidders, the duration of the auction and thus the auctioneer’s
revenue increases. In an experimental study, Caldara (2012) shows that neither risk-loving
bidders nor incorrect beliefs regarding the parameters of the auction (such as the number of
bidders) are necessary for observing revenues that exceed the product’s value and thus the
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expected revenues. Moreover, he finds that revenues move closer to the revenues of the
theoretical model as bidders gain experience. The important role of experience is supported by
Wang and Xu (2013), who analyze bid-level data from a large ascending pay-per-bid auction
website and show that losing bidders stop participating in these auctions while others learn,
continue to bid and make profits.
By contrast, there is little research on descending pay-per-bid auctions, as Gallice (2011) is
the only researcher who derives equilibrium bidding behavior in descending pay-per-bid
auctions. He shows that in equilibrium, only two situations can arise: either the product is
purchased at the starting price, or no bid occurs. The reason is that if at least one bidder is willing
to buy at the starting price, then this bidder will buy immediately; if no bidder is willing to buy at
the starting price, then no one will ever observe the price, and the product will not be sold.
However, contrary to his prediction, Gallice (2011) finds (similar to what ascending pay-per-bid
researchers have found) that actual revenues were well above the expected revenues. He explains
the deviations with bounded rationality of the bidders.
Thus far, there is no study that compares the averages and variances of actual and expected
revenues among pay-per-bid auctions with varying sizes (penny vs. ten-cent) or signs (ascending
vs. descending) of price increments. In the following, we will present the theoretical models on
which our empirical analysis is based.
3. Economic Analysis of Pay-per-Bid Auctions
For both auction formats, ascending and descending pay-per-bid auctions, we use the same
assumptions as Platt et al. (2013) and Augenblick (2012). These assumptions lead to a theoretical
model that is similar to the model that Platt et al. (2013) and Augenblick (2012) developed for the
ascending auction and to a special case of the theoretical model that Gallice (2011) suggested for
the descending auction.
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3.1. Model Assumptions
Risk neutral bidders: We assume throughout the study that there are n risk-neutral bidders.
However, the assumption of risk neutrality is not innocuous. Platt et al. (2013) show that
expected revenues of ascending pay-per-bid auctions are decreasing in the degree of risk
aversion. Expected revenue is lower (higher) when bidders are risk averse (loving) than when
they are risk-neutral. Platt et al. (2013) find evidence for modest degrees of risk-loving
preferences. However, the reported range of estimated degrees of risk aversion is wide (varying
between -0.0017 (for $1,000) and -0.03 (for the 50 free bids)), and the degree of risk aversion
appears to depend on the product that is auctioned off. Moreover, in contrast to ascending pay-
per-bid auctions (Reiner, Brünner, Natter, & Skiera, 2014; Platt et al., 2013,) there are no
estimates of the risk attitudes of bidders in descending pay-per-bid auctions. Therefore, we
assume risk-neutral bidders in the theoretical models of all auction formats.
Common valuations of products: Each bidder values the product to be auctioned off at the
commonly known willingness-to-pay (WTP) of v. For art, antique furniture and other collectors’
items that are typically associated with auctions, the assumption that all bidders value a product
equally is certainly improbable. However, because the products that are offered at pay-per-bid
auctions are brand new products that are readily available at alternative shopping websites or
high street retailers, we believe that the assumption is reasonable. Augenblick (2012) shows that
a theoretical model in which bidders have independent private valuations converges to the full
information common valuation case as the differences in valuation decrease.
Current retail price (CRP) = willingness-to-pay (WTP): Pay-per-bid auction providers
display a product’s CRP for the entire time of the auction. This price is often higher than the
prices that other shopping websites post for the same product. For example, Augenblick (2012)
reports that the average price of Amazon is only 79% of the CRP. However, bidders’ WTP is in
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turn estimated to be 15% to 65% higher than the Amazon price (Platt et al., 2013). These
numbers lead to a range for the WTP that is between 90.85% (1.15 x 79%) and 130.35% (1.65 x
79%) of the CRP. Because this value is posted prominently on the auction website, it may also
serve as an anchor. Therefore, we use the CRP as a proxy for the WTP, which should work well
for cash or vouchers because the CRP is simply equal to the amount of cash or the monetary
value of the voucher.
3.2. Economic Analysis of Ascending Pay-per-Bid Auctions
In the following, we present the baseline model of the ascending pay-per-bid auction
developed by Platt et al. (2013) and Augenblick (2012). There are n bidders. The ascending
auction starts at a price of zero. Each bid increases the price by d and costs b. After each bid, all
bidders (except the current highest bidder) decide whether to place a bid or not. If several bidders
decide to bid, then one of them is randomly selected, pays the bidding fee b and becomes the new
highest bidder. The current price is raised by d. Thus, after q bids, the auction price is qd. If none
of the bidders places a new bid, then the auction ends, and the current highest bidder buys the
product for the current auction price.
Platt et al. (2013) and Augenblick (2012) show that there is a symmetric subgame perfect
equilibrium in mixed strategies; after q-1 bids, every bidder who is not the current highest bidder
places a bid with probability :
(1)
To obtain an intuition for the equilibrium strategy in equation (1), let us first argue why the
behavior of bidders is stochastic or, more technically, why there is no symmetric equilibrium in
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pure strategies. Suppose that the number of bids is low, such that the WTP for a product exceeds
the current price plus the bidding cost: v > qd + b. If a bidder knew that all other bidders would
not bid, then she would bid and make a bargain. As a result, a situation in which no bidder places
a bid cannot be an equilibrium. Similarly, when all bidders always place a bid early in the
auction, it will become advantageous for a bidder to wait and allow the other bidders to pay the
bidding fees until there is a positive probability that the auction will end. Thus, a situation in
which all bidders always bid is also not an equilibrium. Therefore, the only symmetric
equilibrium is in mixed strategies. The probability of making a bid is determined such that
bidders are indifferent between placing a bid and not placing a bid.
The parameter in the equilibrium strategy in equation (1) is the probability that at least one
bidder will place a bid in the first period. This parameter is not uniquely determined in
equilibrium. However, if no one places a bid in the first round, which occurs with probability
, then the auction ends, and the auctioneer can immediately set up a new, identical auction.
If, again, no bidder places a bid, then the auctioneer can restart the auction repeatedly until there
is at least one bid in the first round. In our data set, we only have auctions that attracted at least
one bid. Therefore, we set to concentrate on auctions that have at least one active bidder.
Platt et al. (2013) show that in an ascending auction with WTP v, these bidding strategies lead
to the following expected value and variance of the revenue of one auction Ra:
(2a)
(2b)
The result for the expected revenue can be obtained by the following logic. The total surplus
of auctioneer and bidders together is then the WTP, v. However, in equilibrium, bidders are
indifferent between placing a bid and not bidding. Consequently, bidders are also indifferent
between placing no bid at all and actively participating in the auction. Because placing no bid at
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all yields a utility of zero, participating in the auction must also have an expected utility of zero.
If the bidders’ expected utilities are zero, the entire surplus accrues to the auctioneer and thus, the
auctioneer’s expected revenue is v. The expression for the variance of revenues in equation (2b)
is the variance of a continuous approximation of the distribution of revenues implied by the
bidding strategies in equation (1).
The expectation and variance of revenue presented in equations (2a) and (2b) were derived
for a single auction in which the bidders’ WTP is v. In our empirical analysis, we calculate
expected revenues by averaging revenues of auctions that were conducted during the period from
August 2007 to March 2009. Similarly, the variance is estimated by the sample variance of
revenues from auctions in that period. Because the WTP changed over that period, the relevant
benchmarks are not the conditional moments in equations (2a) and (2b) but the unconditional
expectation and variance given by the following:2
(3a)
(3b)
where E(v) and Var(v) are the expectation and the variance of the WTP, respectively.
The data sets analyzed below include ascending auctions with per-bid price increments of
d = €0.01 and d = €0.10. Therefore, we seek to determine the effect of a change in d on revenues.
From equations (3a) and (3b), we obtain the following predictions:
Prediction 1: An increase in the price increment d reduces the variance of auctioneer revenues in
ascending pay-per-bid auctions.
Prediction 2: An increase in the price increment d leaves the expected revenue in ascending pay-
per-bid auctions unaffected.
2 Here, we use the result that .
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3.3. Economic Analysis of Descending Pay-per-Bid Auctions
For the descending auction, we adapt the theoretical model by Gallice (2011), such that the
assumptions are the same as in the theoretical model by Augenblick (2012) and Platt et al.
(2013). We show below that the main results of Gallice (2011) are not affected by this
modification.
The descending pay-per-bid auction begins at a price, s, which is usually equal to the current
retail price (CRP). The starting price is publicly observable. Each bid decreases the current
auction price by e and costs b. The bidding costs are greater than the price decrement, b > e.3 In
contrast to the ascending auction, the current auction price is not publicly observable. Only the
current bidder can view this price. After observing the current auction price, the bidder can
decide whether to buy the product or not. If she decides to buy, then she pays the current auction
price, and the auction ends. If she decides not to buy, then the auction continues. The other
bidders do not know whether and how often someone has observed the price. Otherwise, a bidder
could count the number of times that the price has been observed and would know the current
price.
Gallice (2011) studies a descending pay-per-bid auction, assuming that bidders have
independently distributed private valuations for the product that is for sale. He shows that when
the highest valuation of a bidder is below the starting price, no bidder will place a bid. We build
on his theoretical model, but in contrast to Gallice (2011), we assume that bidders have
commonly known valuations for the products auctioned and, hence, a common WTP, v, that is
known. If the starting price is excessively high, i.e., v < s - e + b, then no bidder will see the
price, and the product will not be sold in equilibrium. If the starting price is sufficiently low, i.e.,
3 If b were smaller than e, then a bidder could observe the price v/e times and buy for a price of 0. The total bidding
costs of this strategy would be bv/e, which is smaller than the WTP v, given that b < e.
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v > s - e + b, then all bidders will want to see the price, and the first bidder who does so will buy
the product. The highest starting price that attracts participation by rational bidders is = v + e -
b. If a bidder places a bid, then she pays b and observes the price - e = v - b. Thus, the
maximum revenue per auction that the auctioneer can extract from rational bidders is .4
Note that for a given common WTP v, the auctioneer’s revenue in descending auctions is
deterministic. However, as for the ascending auction, the relevant benchmarks for our empirical
results are the unconditional expectation and variance:
(4a)
(4b)
Note that the starting price in the descending pay-per-bid auctions in our data set is the CRP.
We assume that the WTP is equal to the CRP. Because of the bidding cost, the CRP is slightly
above the maximum starting price .5 This characteristic implies that in equilibrium, we should
expect no bids in the descending auctions. This result is clearly at odds with the empirical results
of real descending pay-per-bid auctions in which we observe active participation.
The fact that bidders observe the price although the starting price is above can be explained
by considering their curiosity. If a bidder is curious about the hidden value of the price, then she
might receive some additional utility from lifting the veil and observing the price. If this
additional utility is greater than the difference of bidding costs and price decrement, b-e, then a
curious bidder will place a bid. Even when all bidders are rational (i.e., not curious) but believe
that some bidders are curious, it is rational to participate because curious bidders might have
4 The formal presentation of the equilibrium of the descending pay-per-bid auction and the proof are given in
Appendix A.
5 For the descending auctions in our data set, bidding costs are b=0.49, and the price decrement is e=0.40. Thus, the
maximum starting price is =CRP-0.09, which is slightly below the actually chosen starting price, which is equal to the CRP.
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placed a bid already and it would thus be profitable to place the next bid.6 However, because the
difference between the true starting price and the maximum starting price is minuscule
compared to the average CRP of the products sold in descending pay-per-bid auctions (€153.48),
we assume that the auctioneer sets the maximum starting price at .
It is easy to observe from equations (4a) and (4b) that the bidding costs, b, and the price
decrement, e, do not affect expected revenue and the variance of revenue. Unfortunately, neither
the bidding costs nor the price decrement was altered during the time period that our sample
encompasses. Therefore, there are no descending auction counterparts to Predictions 1 and 2 for
ascending auctions.
3.4. Theoretical Comparison of Ascending and Descending Pay-per-Bid Auctions
Having derived the revenues for both auction formats, we can now compare revenues per
auction and their variance for ascending and descending pay-per-bid auctions. Examining
equations (3a) – (4b), we obtain the following predictions:
Prediction 3: The variance of an auctioneer's revenue per auction is higher in ascending pay-per-
bid auctions than in descending auctions.
Prediction 4: Ascending pay-per-bid auctions generate the same expected revenues as descending
auctions.
4. Empirical Study of Ascending Auctions
Based on our economic analyses of ascending and descending auctions, we now aim to
empirically test our predictions (1-4) by comparing the expected revenues (serving as a
benchmark) derived from the theoretical model with actual revenues and by explaining the
resulting differences.
6 The websites of descending pay-per-bid auctioneers display the results of past auctions. Bidders can observe that
past auctions attracted bids and that the product was finally sold at a price below the current retail price. Thus, a rational bidder can conclude that there must be some curious bidders.
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In the following, we will first analyze ascending and descending auctions separately (Section
4 and 5). In Section 6, we will study the differences between ascending and descending pay-per-
bid auctions.
4.1. Data
We collected data from a European ascending pay-per-bid auctioneer that provided us with
two unique data sets. In contrast to a platform such as eBay that includes three parties
(auctioneer, buyer, and seller), the auctioneer is also the seller. Additionally, the auctioneer sells
only brand new products that are currently available at retailers (i.e., common collectibles). Used
products and older-generation products are not auctioned.
The first data set (A1) contains the results of all ten-cent (N=42,042) and penny (N=1,112)
ascending auctions from December 2007 to November 2008 (43,154 auctions in total). For each
completed auction, we received information about what product was auctioned, the final price,
the current retail price (CRP), the end time and the number of bids placed by the winners of the
auction. All auctions start at a price of €0.00, and each bid costs €0.50.
The second data set (A2) contains the results of 1,460 ascending auctions completed in March
2009, plus additional information regarding the bidding histories of these auctions, including
949,750 bids and their respective bidders. Data set A2 also includes information regarding the
participating bidders beyond these bids, such as their overall bidding experience with the
auctioneer (e.g., the number of auctions won, the number of auctions participated in) and
demographic information.
The two data sets differ in their numbers of auctions and in the details that are provided for
each auction. Data set A1 contains considerably more auctions, whereas data set A2 provides
more details regarding all bids (e.g., bidding time, nickname of bidder) and information regarding
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bidders beyond their behavior in these auctions (their first bidding date, the number of auctions
with bids placed, the number of auctions won, total bids placed, gender and age).
All data sets include information on the auction end time, the nickname of the winner, the
number of bids made by the winner, the total number of bids made (by the winner and the losers),
the product sold and its CRP. According to the auctioneer, the CRP represents an average price
value for the product on the basis of other online retailers. Table 2 provides an overview of the
product categories of the auctioned products from both data sets.
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Table 2
Description of the Data Sets
Product Category Typical Products in Category
Ascending Auction
(A1)
Ascending Auction
(A2)
# Ten-Cent
Auctions
# Penny
Auctions
# Ten-Cent
Auctions
# Penny
Auctions
Video Game Console Nintendo DS, Nintendo Wii, PSP, PS3, Xbox 360 10,465 1 422 0
Software Programs, PC games, Video games 8,949 1 244 0
4.2. Comparison of Actual and Expected Revenues per Auction
First, we compare actual revenues and expected revenues. For all revenues, we calculate
the average revenues across all categories standardized by their CRP, i.e. we divided the
revenues per auction by the corresponding CRP. We use equation (2a) to calculate the
expected revenues and use a t-test to compare them with actual revenues. To perform the t-
test, we also apply the variances of standardized expected revenues from equation (2b). Table
3 depicts the standardized means of the actual and expected revenues per auction as well as
the percentage difference across all categories for both the ten-cent auctions and the penny
auctions. As noted above, we assume that the WTP is equal to the CRP. This assumption is
certainly valid for products such as vouchers or cash, as these products are of a defined value
that is common to everyone (i.e., every bidder values a €50 voucher or €50 in cash equally).
However, this assumption may also hold for the remaining products: all auctioned products
are brand new, are in their original packaging and are currently sold at competitive retailers.
Additionally, the CRP represents an average price value for each product from common
online retailers.
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Table 3
Comparison of Means of Actual and Expected Standardized Revenues per Auction from
Ascending Auctions
Product
Category
Ten-Cent Auction
Penny Auction
N Actual
Revenue
Expected
Revenue Δ-% N
Actual
Revenue
Expected
Revenue Δ-%
Cash 11 2.07 1.00 *** 107%
Voucher 43 0.98 1.00 n.s.
185 4.21 1.00 *** 321%
Video Game
Console 10,887 1.75 1.00 *** 75%
Fast-Moving
Electronic
Appliances
1,257 1.34 1.00 *** 34%
11 0.73 1.00 n.s.
Software 9,190 1.26 1.00 *** 26%
Computer
Hardware 2,579 0.94 1.00 *** -6%
510 1.77 1.00 *** 77%
DVD 922 0.94 1.00 n.s. -6%
GPS 623 0.91 1.00 ** -9%
525 1.58 1.00 *** 58%
Toys 1,389 0.90 1.00 *** -10%
Home
Appliances 2,266 0.90 1.00 *** -10%
13 0.76 1.00 n.s.
Perfume 1,408 0.87 1.00 *** -13%
Small
Electronic
Goods
2,096 0.86 1.00 *** -14%
66 1.31 1.00 ** 31%
TV + Audio-
visual 639 0.83 1.00 *** -17%
158 1.21 1.00 * 21%
Computer
Accessories 4,517 0.75 1.00 *** -26%
Housewares 407 0.74 1.00 *** -26%
Others 1,491 0.72 1.00 *** -28%
Jewelry 3,276 0.21 1.00 *** -79%
TOTAL 43,057 1.12 1.00 12% 1.557 1.90 1.00 *** 90%
Δ-%: percentage differences between the means of actual and expected standardized revenues; positive differences are
illustrated in green cells and negative differences in red. All revenues are standardized. Standardized revenue is defined as revenue / CRP; CRP: current retail price;
